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Geometria starożytna i filozofia Platona na podstawie Komentarza Pappusa do X księgi "Elementów" Euklidesa

Król Z.

Kwartalnik Historii Nauki i Techniki

2006

R. 51, nr 3/4

169-203

The article is treating of a new interpretation of ancient geometry (part I) and is willing to explain several mathematical and historical conceptions that were presented in Pappus' Comment on the X'h Book of 'Elements' of Euclid (part 11). Euclid's Elements were a kind of 'intuitive model', quite different from the contemporary one. Elements were divested of the 'infinitespace' notion. Reconstruction of the hermeneutic horizon of the ancient mathematics lets us explain structure and mathematics presented in the columns ofthe Xth book of Elements. The following subjects were handled: 1. reasons for elimination of the Euclid's ' infinite space' notion and substitutin.s it for Plato's Diad in ancient times, 2. basing geometry and searches over the incommensurable magnitudes on one distinguished line together with mathematical consequences, 3. differences in the way of thinking of ancient and contemporary mathematician. Scientific studies let qualify from the historical point of view the share in development of the incommensurable magnitudes theories presented by Theaetetus of Athens, Apollonius of Perga, Euclid and Eudoxus. In the article there is also presented a reconstruction of the mathematical contents of the lost Apollonius' treatise on incommensu- able magnitudes. A traditionally established pattern of the development of geometry, according to which Euclidean geometry used to extend as theory basing on relatively unalterable outfit of the fundamental intuition as, for instance, Euclid's infinite space, continuum intuitions and metric intuitions (what important, the first revolutionary change was a discovery of non -Euclidean geometry in the XIXth century) -cannot be sustained.

Wincenty Lutosławski - człowiek i dzieło

Zaborowski R.

Kwartalnik Historii Nauki i Techniki

2004

R. 49, nr 1

65--82

Wincenty Lutosławski was born in Warsaw, on June 6, 1863. His initial choice of university studies was chemistry and he got his first diploma for the thesis Das Gesetz der Beschleunigung der Esterbildung, ein Beitrag zur chemischen Dynamik (Halle 1885). Later, in 1885, he moved on to study at a faculty of history and philology under Gustav Teichmiiller; and he obtained a master’s degree in philosophy for the thesis Erhaltung und Untergang der Staatsverfassungen nach Plato, Aristoteles und Machiavelli (Dorpat, 1887, second edition - Breslau 1888). Lutosławski spent the next ten years studying Plato’s logic (The Origin and Growth o f Plato s Logic with an Account of Plato’s Style and o f the Chronology o f his Writings, London 1897, second edition 1905, reprinted in 1983). In the years 1899-1900 he lectured at the Chair of Philosophy of the Jagiellonian University in Cracow, and in the years 1901-1902 he gave lectures at universities in Lausanne (on Mickiewicz) and in Geneva (on Plato). Lutosławski spent the next few years travelling around the USA and Europe. In 1919 he was offered the Chair of Philosophy at the Stefan Batory University in Wilno (Vilnius). After retiring in 1929, he lived for two years in Paris, then for some time in the vicinity of Cieszyn, and since 1934 until his death in Cracow. He died on December 28, 1954. The fullest bibliography of Lutosławski’s work in the years 1885-1952 covers a total of 820 items, out of which ninety six appeared as selfstanding publications; he published in Polish, German, English, French, Spanish, Italian and Russian (he also knew Grek and Latin). The current paper discusses three areas of Lutosławskie research: Plato, Polish romanticists, and his own philosophical system. Lutosławski is best known for his discoveries on the chronology of Plato’s works, but it must be noted that tackling the issue of chronology was but ”a footnote to a footnote” and was of secondary importance to Lutosławskie main concern, namely the study of evolution of Plato’s thought. Lutosławski discovered that after Plato had created idealism, he went beyond it and moved towards spiritualism. However, Lutosławski’s discovery was disregarded by his critics. Fifty years later, at the Tenth Congress of Philosophy in Amsterdam in 1948, Lutosławski once again described in his paper ’’the momentous question of Plato’s change of mind, his giving up completely the idealism and communism of the Republic, and proclaiming the individual souls as the only real substances.” Lutoslawski’s attachment to Polish romanticists stemmed from his conviction of their unique worth and importance, which he wrote about in his books published in foreign languages, thus becoming an impassioned promoter of Polish culture abroad (cf. Volonte et liberte, Paris 1913, Pre-existence and Re-incarnation, London 1928, The Knowledge o f Reality, Cambridge 1930, Preesistenza e reincamazione, Torino 1931). He delivered two papers devoted to this subject-matter at the Fourth International Congrees of Philosophy in Bologna in 1911 (W. Lutosławski, La nation comme realite metaphysique, in; Atti del IV Congresso internazionale di filosofia, vol. 3, Bolgona 1911, pp. 449-454; W. Lutosławski, Le messiansimepolonais, in: Atti del IV Congresso internazionale di filosofia, vol. 3, Bolgona 1911, pp. 186-192), while at the Ninth International Congress of Philosophy in Paris (1937) he gave a paper devoted to the work of Adam Mickiewicz (W. Lutosławski, L ’extase mystique, extrait des Travaux de IXe Congres International de Philosophie (Congres Descartes), Paris 1-6 Aout 1937, pp. 149-157). In that last paper, Lutsosławski argued that if Mickiewicz stopped writing poetry at the age of thirty-five and devoted himself completely to public and religious activity, this was because he had abandoned it voluntarily, under the influence of the experience described in his last poetic work Widzenie (The Vision). Lutosławski considered himself more of a philosopher rather than just as a historian of philosophy. Initially he reduced all forms of Weltanschauung to only two: ’’The individualist says ‘I do most really exist, and besides me other beings like myself.’ The universalist answers: ‘Only the whole does really exist, and I am but a manifestion of being’”. As time went by, Lustoławski distinguished four such forms: materialism, idealism, pantheism and monadology, otherwise referred to as individualism, spiritualism or eleutherism. The last term derives from the Greek word eleutheria (freedom), which means that eleutherism is a view based on the recognition of the creative free will.